Electromagnetic inverse scattering problems

Abstract

The inverse scattering technique is one of the most important approaches for attaining a quantitative description of the electrical and geometrical characteristics of the scatterer, and has found vast number of applications, such as echolocation, geophysical survey, remote sensing, nondestructive testing, biomedical imaging and diagnosis, quantum field theory, and military surveillance.

This work addresses the electromagnetic inverse scattering problems, i.e., to reconstruct, from the scattered electromagnetic signal, the internal constitution of the domain of interest. The candidate's original contribution covers both the full-data and the phaseless data measurement, and both point-like and extended scatterers. For the inverse scattering problem of extended scatterers with the measurement data being the scattered electromagnetic field, the candidate generalized the full-data subspace-based optimization method (FD-SOM) to the transverse electric case. In addition, a comparison among the variants of FD-SOM is provided, which indicates the optimum choice for specific problems. For the phaseless-data inverse scattering problems, the candidate proposed the phaseless-data subspace-based optimization method (PD-SOM), which deals with the inverse scattering problem of reconstructing extended scatterers with intensity-only measurement. For the phaseless imaging of point-like objects, the candidate formulated the problem in the emerging framework of compressive sensing (CS) and proposed the method of compressive phaseless imaging through minimizing a convex functional. The efficiency and robustness of the aforementioned methods have been verified by numerical experiments.